Question 1

The national norm for third graders on a standardized test of reading achievement is a score of 27. Mrs. Johnson obtains the mean score on the test for a random sampling of third graders from her school district. The results for Mrs. Johnson's sample are $\overline{X} = 33.1, s_X = 5.2 and n=30$ (a) Construct the 95% confidence interval for her population mean score. (b) Construct the 99% confidence interval for her population mean score. (c) What generalization is illustrated by a comparison of the answers to (a) and (b)?

Accepted Answer

(a) 
  
 (b) 
  
 (c) the higher the level of confidence, the wider the interval

Question 2

A random sample of 20 students at Alpha College is asked how many hours a week they study on the average. The following are the results: 
  
 and 
  
 Construct the 95% confidence interval for the mean hours studied per week for the entire student body. What does the 95% refer to? Be very explicit and precise in your answer.

Accepted Answer

If the study were repeated many times, 95% of the intervals constructed in the same way would include 
  
.

Question 3

The directors of a charitable organization wish to compare the effectiveness of two programs for training their phone solicitors. Thirty-one volunteers are randomly divided into two groups. Group A is trained using method A and Group B using method B. The following are the results for this year's fund drive (in dollars per volunteer):

Accepted Answer

The answer of The directors of a charitable organization wish...

Question 4

The following are the achievement test results for 15 matched pairs taught by Method A and Method B.   
(a)Construct the 95% confidence interval for $(\mu_A - \mu_B)$. 
(b)Ignore thecorrelation coefficient and treat the two samples as though they were independent. Construct the 95% confidence interval for $(\mu_A - \mu_B)$. 
(c)What does a comparison of the answers to (a) and (b) suggest concerning the effect on interval estimates of using samples?

Accepted Answer

The answer of The following are the achievement test results...

Question 5

Random samples are selected and the 95% confidence interval for  is constructed. It runs from -3.1 to 9.4.  
(a) If a two-tailed test were used at  would a significant difference be found between  and  Explain. 
(b) Give the 95% confidence interval for

Accepted Answer

The answer of Random samples are selected and the 95%...

Question 6

Determine the 95% confidence interval for  in each of the following cases:
a)  b)  c)  d) A comparison of the widths of the intervals obtained in (a), (b), and (c) suggests what generalization concerning the sampling variation of the correlation coefficient?

Accepted Answer

The answer of Determine the 95% confidence interval for ...

Question 7

Which statement is true?

Accepted Answer

Hypothesis testing is used to determine whether there is a statistically significant difference between two or more groups. Estimation is used to estimate the value of a population parameter. While hypothesis testing and estimation are related, they are not interchangeable.

Question 8

Confidence intervals of a parameter are preferred over hypothesis testing when

Accepted Answer

Confidence intervals provide a range of plausible values for a parameter, which is useful when there is no specific value of interest to test against, unlike hypothesis testing which focuses on testing a specific hypothesis.

Question 9

Which statement, if any, is incorrect?

Accepted Answer

All of the statements are true.

Question 10

The rule for constructing a confidence interval of the population mean is

Accepted Answer

The answer of The rule for constructing a confidence interval...

Question 11

Confidence intervals are generally to be preferred over point estimates because confidence intervals

Accepted Answer

Confidence intervals account for sampling error by providing a range of values within which the true parameter is likely to fall, offering more information than a single point estimate.

Question 12

For a random sample of 100 cases,  
 and
  
. The 95% confidence interval for 
  
 would run approximately from

Accepted Answer

The answer of For a random sample of 100 cases,...

Question 13

We construct a 90% confidence interval for P, the population proportion of freshmen able to pass a proposed English placement exam. The sample interval runs from .43 to .49. This tells us that

Accepted Answer

A 90% confidence interval means that if we were to take many samples and construct intervals in the same way, 90% of those intervals would contain the true population proportion P.

Question 14

Which set of circumstances is most likely to result in a narrow confidence interval?

Accepted Answer

A large sample size (n) reduces the standard error, and a lower confidence level (.95) results in a smaller margin of error, both contributing to a narrower confidence interval.

Question 15

For a confidence interval of  
, an interval of lesser width results

Accepted Answer

The answer of For a confidence interval of  
,...

Question 16

The advantage of expressing a confidence interval in terms of the number of standard deviations of the variable is that

Accepted Answer

Expressing a confidence interval in terms of standard deviations accounts for the variability of the data, making it easier to interpret the importance of the interval relative to the data's spread.

Question 17

The rule for constructing a confidence interval of the difference between two means is

Accepted Answer

The answer of The rule for constructing a confidence interval...

Question 18

In establishing a confidence interval for the difference between two means, selecting a confidence level of .95 rather than a confidence level of .90 implies that

Accepted Answer

A higher confidence level results in a wider interval, as it requires more range to ensure the true parameter is captured with greater certainty.

Question 19

Which factor will not affect the width of a confidence interval constructed to estimate the difference between two population means?

Accepted Answer

The answer of Which factor will not affect the width...

Question 20

A 95% confidence interval for  
 runs from -2 to +6. From this we can infer that

Accepted Answer

The answer of A 95% confidence interval for  
...

Quiz 17: An Alternative to Hypothesis Testing: Confidence Intervals

Random samples are selected and the 95% confidence interval for is constructed. It runs from -3.1 to 9.4. (a) If a two-tailed test were used at would a significant difference be found between and Explain. (b) Give the 95% confidence interval for

Determine the 95% confidence interval for in each of the following cases: a) b) c) d) A comparison of the widths of the intervals obtained in (a), (b), and (c) suggests what generalization concerning the sampling variation of the correlation coefficient?